2.10. Use Ito’s formula (2.4) for the following:

• Since X = t+W(t) satisfies dX = dt+dW, confirm that Y = sinhX satisfies dY = 
12 Y +

1+Y2 
dt+

1+Y2dW .
• For the above Ito process Y, deduce dZ for Ito process Z = Y3 .
Recall that d dx sinhx = coshx , d dx coshx = sinhx, and cosh2x = 1+sinh2x .